Presently, in 3GPP RAN LTE (long term evolution) studies are conducted on the preamble a mobile station first transmits in random access between mobile stations and a base station in RACH (Random Access Channel) For the preamble, a known sequence between the mobile stations and the base station is used. The base station needs to detect different preambles from a plurality of mobile stations based on correlation values of the sequences and detect reception timings with accuracy, so that the sequences used as preambles should have good autocorrelation characteristics and cross-correlation characteristics, and have low PAPR (Peak to Average Power Ratio).
One of sequences of good autocorrelation characteristics and cross-correlation characteristics and of low PAPR is a Zadoff-Chu sequence (hereinafter simply “ZC sequence”) (see Non-Patent document 1). A ZC sequence is represented by ar(k) in equation 1. Here, N is the sequence length and r is the sequence number (N and r are coprime), and q is an arbitrary integer. The feature of a ZC sequence includes good autocorrelation characteristics and relatively little cross-correlation characteristics, that is, the cross-correlation is √N if N is a prime number.
                    (                  Equation          ⁢                                          ⁢          1                )                                                                                  a            r                    ⁡                      (            k            )                          =                  {                                                                                          ⅇ                                                                  -                        j                                            ⁢                                                                        2                          ⁢                          π                          ⁢                                                                                                          ⁢                          r                                                N                                            ⁢                                              (                                                                                                            k                              2                                                        /                            2                                                    +                          qk                                                )                                                                              ,                                                                              N                  ⁢                                      :                                    ⁢                  even                                                                                                                          ⅇ                                                                  -                        j                                            ⁢                                                                        2                          ⁢                          π                          ⁢                                                                                                          ⁢                          r                                                N                                            ⁢                                              (                                                                                                            k                              ⁡                                                              (                                                                  k                                  +                                  1                                                                )                                                                                      /                            2                                                    +                          qk                                                )                                                                              ,                                                                              N                  ⁢                                      :                                    ⁢                  odd                                                                                        [        1        ]            
Further, in 3GPP RAN LTE, studies are conducted on a cyclic-shifted ZC sequence (hereinafter, simply “CS-ZC sequence”), which is a sequence where a ZC sequence is cyclically shifted (see Non-patent Document 2). As shown in FIG. 1, CS-ZC sequences are generated by cyclically shifting one ZC sequence. FIG. 1 shows an example with seven CS-ZC sequences, that is, CS-ZC sequences #1 to #7 that are generated by cyclically shifting ZC sequence #1 (shift zero) of sequence length N=293 by the amount of shift Δ=36. These CS-ZC sequences #1 to #7 are orthogonal to each other if the propagation delay time of a mobile station does not exceed the amount of shift and the cross-correlation between the sequences is zero, so that the accuracy of preamble detection is high when a CS-ZC sequence is used as a preamble.
Further, in 3GPP RAN LTE, the preamble length that can support a cell radius up to 30 km is studied. To secure a received S/N needed for preamble detection, it is necessary to make the preamble length longer and increase the energy of the preamble signal when the cell radius is greater and propagation attenuation increases. That is, in cases where a CS-ZC sequence is used as a preamble, it is necessary to make the sequence length of a ZC sequence longer when the cell radius is greater.
Here, as a method of acquiring the sequence length according to the cell radius with regards to a ZC sequence, two methods, that is, a method of extending sequence length N (i.e. sequence extension method) and a method of repeating a ZC sequence having sequence length N (i.e. sequence repetition method) are studied (see Non-patent Documents 3 and 4). If the sequence extension method is used in these methods, it is possible to generate many more ZC sequences and obtain a larger number of ZC sequences that can be used in the entire communication system. That is, the sequence extension method provides an advantage of increasing the reuse factor of sequences and making cell planning easy. The reuse factor equals the value dividing the number of ZC sequences that can be used in the entire communication system by the number of ZC sequences assigned per cell, and is proportional to the number of ZC sequences. In cases where a ZC sequence whose sequence length N is a prime number and whose correlation characteristics are good is used, N−1 ZC sequences can be generated, and the reuse factor is proportional to sequence length N. Consequently, as a method for acquiring the sequence length according to the cell radius with regards to ZC sequences, the sequence extension method becomes more focus of attention.    Non-patent Document 1: Popvic, “Generalized chirp-like polyphase sequences with optimal correlation properties,” IEEE Transactions on information Theory, July 1992, 1406-1409    Non-patent Document 2: 3GPP, R1-060046, NTT DoCoMo, “Orthogonal Pilot Channel Structure in E-UTRA Uplink”    Non-patent Document 3: 3GPP, R1-062004, Texas Instruments, “Non-Synchronized Random Access Sequence Design for E-UTRA”    Non-patent Document 4: 3GPP, R1-062306, LG, “RACH Sequence Extension Methods for Large Cell Deployment”